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Title: Dynamical determinants and their applications
Author: Felton, Philip
ISNI:       0000 0004 2735 6883
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2012
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This thesis is concerned with situations where we can define trace-class transfer oper- ators, and extract useful information from their determinants. The first topic is on Lyapunov exponents of random products of matrices. We obtain a new expression for the Lyapunov exponent of a continuous family of matrices, and a slightly different version of existing work for the discrete case. The second topic explores possibilities of using similar theory to approximate eigen- functions of the Laplacian for surfaces of constant negative curvature. The third topic gives a variety of approximations of Mahler measures, which occur in many different areas of mathematics, by manipulating the integrals into a form that can be numerically integrated using work of Pollicott and Jenkinson. The final topic of the thesis works out the details of earlier ideas of Pollicott, to give a method for the numerical approximation of entropy rates of hidden Markov processes.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics